1// Copyright 2011 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package math
6
7/*
8	Floating-point tangent.
9*/
10
11// The original C code, the long comment, and the constants
12// below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
13// available from http://www.netlib.org/cephes/cmath.tgz.
14// The go code is a simplified version of the original C.
15//
16//      tan.c
17//
18//      Circular tangent
19//
20// SYNOPSIS:
21//
22// double x, y, tan();
23// y = tan( x );
24//
25// DESCRIPTION:
26//
27// Returns the circular tangent of the radian argument x.
28//
29// Range reduction is modulo pi/4.  A rational function
30//       x + x**3 P(x**2)/Q(x**2)
31// is employed in the basic interval [0, pi/4].
32//
33// ACCURACY:
34//                      Relative error:
35// arithmetic   domain     # trials      peak         rms
36//    DEC      +-1.07e9      44000      4.1e-17     1.0e-17
37//    IEEE     +-1.07e9      30000      2.9e-16     8.1e-17
38//
39// Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9.  The loss
40// is not gradual, but jumps suddenly to about 1 part in 10e7.  Results may
41// be meaningless for x > 2**49 = 5.6e14.
42// [Accuracy loss statement from sin.go comments.]
43//
44// Cephes Math Library Release 2.8:  June, 2000
45// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
46//
47// The readme file at http://netlib.sandia.gov/cephes/ says:
48//    Some software in this archive may be from the book _Methods and
49// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
50// International, 1989) or from the Cephes Mathematical Library, a
51// commercial product. In either event, it is copyrighted by the author.
52// What you see here may be used freely but it comes with no support or
53// guarantee.
54//
55//   The two known misprints in the book are repaired here in the
56// source listings for the gamma function and the incomplete beta
57// integral.
58//
59//   Stephen L. Moshier
60//   moshier@na-net.ornl.gov
61
62// tan coefficients
63var _tanP = [...]float64{
64	-1.30936939181383777646e4, // 0xc0c992d8d24f3f38
65	1.15351664838587416140e6,  // 0x413199eca5fc9ddd
66	-1.79565251976484877988e7, // 0xc1711fead3299176
67}
68var _tanQ = [...]float64{
69	1.00000000000000000000e0,
70	1.36812963470692954678e4,  //0x40cab8a5eeb36572
71	-1.32089234440210967447e6, //0xc13427bc582abc96
72	2.50083801823357915839e7,  //0x4177d98fc2ead8ef
73	-5.38695755929454629881e7, //0xc189afe03cbe5a31
74}
75
76// Tan returns the tangent of the radian argument x.
77//
78// Special cases are:
79//	Tan(±0) = ±0
80//	Tan(±Inf) = NaN
81//	Tan(NaN) = NaN
82
83//extern tan
84func libc_tan(float64) float64
85
86func Tan(x float64) float64 {
87	return libc_tan(x)
88}
89
90func tan(x float64) float64 {
91	const (
92		PI4A = 7.85398125648498535156e-1  // 0x3fe921fb40000000, Pi/4 split into three parts
93		PI4B = 3.77489470793079817668e-8  // 0x3e64442d00000000,
94		PI4C = 2.69515142907905952645e-15 // 0x3ce8469898cc5170,
95	)
96	// special cases
97	switch {
98	case x == 0 || IsNaN(x):
99		return x // return ±0 || NaN()
100	case IsInf(x, 0):
101		return NaN()
102	}
103
104	// make argument positive but save the sign
105	sign := false
106	if x < 0 {
107		x = -x
108		sign = true
109	}
110	var j uint64
111	var y, z float64
112	if x >= reduceThreshold {
113		j, z = trigReduce(x)
114	} else {
115		j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
116		y = float64(j)           // integer part of x/(Pi/4), as float
117
118		/* map zeros and singularities to origin */
119		if j&1 == 1 {
120			j++
121			y++
122		}
123
124		z = ((x - y*PI4A) - y*PI4B) - y*PI4C
125	}
126	zz := z * z
127
128	if zz > 1e-14 {
129		y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
130	} else {
131		y = z
132	}
133	if j&2 == 2 {
134		y = -1 / y
135	}
136	if sign {
137		y = -y
138	}
139	return y
140}
141